We introduce the notion of a retro Banach frame relative to a bounded $b$-linear functional in $n$-Banach space and see that the sum of two retro Banach frames in $n$-Banach space with different reconstructions operators is also a retro Banach frame in $n$-Banach space. Also, we define retro Banach Bessel sequence with respect to a bounded $b$-linear functional in $n$-Banach space. A necessary and sufficient condition for the stability of retro Banach frame with respect to bounded $b$-linear functional in $n$-Banach space is being obtained. Further, we prove that retro Banach frame with respect to bounded $b$-linear functional in $n$-Banach space is stable under perturbation of frame elements by positively confined sequence of scalars. In $n$-Banach space, some perturbation results of retro Banach frame with the help of bounded $b$-linear functional in $n$-Banach space have been studied. Finally, we give a sufficient condition for finite sum of retro Banach frames to be a retro Banach frame in $n$-Banach space. At the end, we discuss retro Banach frame with respect to a bounded $b$-linear functional in Cartesian product of two $n$-Banach spaces.
原文链接
分享
引用
